Suppose we determine 20 girls with low childhood SES and find out mean age at the menarche of 13.4 years with standard deviation of 1.4 years. We determine an additional 30 girls with high childhood SES and find out a mean age at menarche of 12.9 years with the standard deviation of 1.5 years. Suppose that the underlying variance of age at menarche for girls with low childhood SES and girls with high childhood SES is the same. How many participants should be enrolled in each group in a future study if
(a) The true mean difference in age at menarche between girls with low- and high-childhood-SES is 0.5 years,
(b) Standard deviation of age at menarche is 1.5 years within each group,
(c) An equal number of girls are in each group, and
(d) We would like to have a 90% chance of detecting a significant difference between the girls with high- and low- childhood SES?